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• W4207025529 endingPage "103700" @default.
• W4207025529 startingPage "103700" @default.
• W4207025529 abstract "This paper extends the multi-level hp-approach—previously introduced for the isotropic refinement of quadrilateral and hexahedral elements—to the anisotropic refinement of quadrilateral and triangular meshes. To this end, this work first introduces anisotropic split operators for the hierarchical refine-by-superposition concept. For quadrilateral cells, the well-known anisotropic h2-split is used. For the anisotropic refinement of triangular cells, a novel split along the barycentric mid-lines is introduced, which minimizes the number of new cells without distorting their shape. Second, it is shown that the isotropic multi-level hp-approach of handling hanging nodes is not directly applicable in the case of directional refinement. For this reason, this work analyses the requirements of a valid fe-basis on anisotropically refined, irregular multi-level meshes and by this generalizes the isotropic multi-level hp-concept. On this basis, an algorithmic realization is derived demonstrating that the applied refine-by-superposition idea carries the implementational simplicity and the native support of arbitrary irregular meshes to anisotropic refinements. A systematic study of benchmarks featuring vertex-, edge-, and edge-vertex singularities as well as boundary layers shows that these advantages come neither at the expense of the approximation quality, nor the sparsity or conditioning of the final equation system. Further, an ad hoc edge-based indication scheme is introduced that reliably guides the place and the direction of the anisotropic refinement process even on unstructured meshes. The presented results qualify the proposed approach as an automatic, anisotropic multi-level hp-refinement method for quadrilateral and triangular meshes, coming at a marginal implementational complexity and without any restrictions due to arbitrary hanging nodes and the associated dead-lock problems." @default.
• W4207025529 created "2022-01-26" @default.
• W4207025529 creator A5012231527 @default.
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• W4207025529 creator A5046623912 @default.
• W4207025529 creator A5082045365 @default.
• W4207025529 date "2022-06-01" @default.
• W4207025529 modified "2023-09-26" @default.
• W4207025529 title "Anisotropic multi-level hp-refinement for quadrilateral and triangular meshes" @default.
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• W4207025529 doi "https://doi.org/10.1016/j.finel.2021.103700" @default.
• W4207025529 hasPublicationYear "2022" @default.
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